A particle moves according to a law of motion  s = f(t), t ≥ 0,  where t is measured in seconds and s in feet. f(t) = t3 − 15t2 + 72t (a) Find the velocity at time t. v(t) =     (b) What is the velocity after 5 s? v(5) = ft/s (c) When is the particle at rest? t = s (smaller value) t = s (larger value) (d) When is the particle moving in the positive direction? (Enter your answer in interval notation.) t     (e) Find the total distance traveled during the first 8 s. ft

Q: A new and powerful robotic aircraft is observed moving along a straight line parallel to the x axis.…

A:

Q: A particle moves along the x axis according to the equation x(t) = 4t+ 3t, where x is in meters and…

A:

Q: The instantaneous speed of a particle moving along one straight line is v(t) = ate"2t where the…

A:

Q: An object moving with uniform acceleration has a velocity of 12.0 cm/s in the positive x-direction…

A:

Q: Using quantitative graphical analysis, find Max's displacement from his initial position at the…

A: Analyze the following figure. a) Max’s displacement can be determined by the given graph’s area as…

Q: The relationship between the velocity of a body moving along the x-axis and time is given by…

A:

Q: A rock weighing 9.5 kg is been thrown from a tall building with an initial velocity of 65 mm/s. If…

A:

Q: An object has an initial velocity 4.3î + -3.7j m/s. Over a v1 = period of time t= 1.4 s, its…

A: Given, v1→=4.3i^-3.7j^v2→=-2i^+0.5j^  t= 1.4 s

Q: A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in…

A: When acceleration is positive particle will speed up

Q: The velocity-time graph that describes the velocity of an object with time is given as in the figure…

A: a = 98.5 b = 124.6 c = 57

Q: A red train travelling at 72 km/h and a green train travelling at 144 km/h are headed toward each…

A:

Q: An object's position as a function of time is given by the expression; x(t) = 14.7/(t+1) + 2.9t3 -…

A:

Q: The motion of a particle is given by V= 2t3 +3t2 +6 , where V is the velocity in m/s and t is time…

A:

Q: The velocity of a particle is defined by the equation v=8t^2+4t+1 where v is in m/min and t is in…

A: In this question we have to find the distance travelled after 60 s. Please give positive feedback if…

Q: A spacecraft starts from rest, and makes a journey to a destination 355000 km from its starting…

A:

Q: A particle moving along the x axis with constant acceleration has a velocity of vy = 41.0 cm/s at t…

A: Given that  A particle moving along the x axis with constant acceleration has a velocity of Vy =…

Q: Suppose that a movie is being filmed in some city. An action shot requires an object to be thrown…

A:

Q: in the figure shown, calculate the average acceleration for the time interval t= 0 to t = 6 v (m/s)…

A:

Q: At t = 0, a train approaching a station begins decelerating from a speed of 80 miles/hour according…

A: (a) . At t= 0 , the train starting deaccelerating from a speed of 80 miles/hr. So, at t= 0 , the…

Q: where t is the number of seconds since observations began. 11. During the time interval from t = 0…

A:

Q: For a water balloon launched from a 4949-meter overlook with an initial vertical velocity of…

A:

Q: A particle moves along the x axis according to the equation x(t) = 4t + 3t, where x is in meters and…

A: given that x = 4 t + 3 t3   average velocity = x2 - x1 / t2 - t1 x(3) = 4 x3 + 3 x 33 = 12 + 81 = 93…

Q: The speed of a bullet as it travels down the barrel of a rifle toward the opening is given by v ! (-…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: A graph of position versus time for a certain particle moving along the x- axis is shown. x (m) 10…

A:

Q: The x-coordinate of a particle in curvilinear motion is given by x = 4.7t - 3.1t where x is in feet…

A: Given values,

Q: The motion of a dog is observed to be given by the function = (1.28 m/s²) t²-[(0.66 m/s³) t³-2.99…

A:

Q: A particle is moving along a line with position given by s(t)=t3−(9/2(t2 ))+6t−5 measured in meters,…

A:

Q: A particle moves according to a law of motion s = f(t), t 2 0, where t is measured in seconds and s…

A: Given particle moves in s = 0.01t4-0.03t3 a) Hence the velocity of the particle is  v = dsdt = 0.04…

Q: A race car moves such that its position fits the relationship x = (6.0 m/s)t + (0.80 m/s³)t3 where x…

A: Given data: Position of the car,  x=6.0 m/st+0.80 m/s3t3

Q: when the projection angle equals (MCQ) art I For Q1) & Q2) The histogram shown beside, gives the…

A: Q.(1 )  Distance travelled in time interval [0.2 ; 0.4] s will be equal to area under v-t diagram .…

Q: A spacecraft starts from rest, and makes a journey to a destination 252000 km from its starting…

A:

Q: The speed of an object moving with uniform acceleration in the + x direction is 23 cm / s and the x…

A: Given data: The initial position of the object is 14 cm. The final position of the object is -8 cm.…

Q: Due to continental drift, the North American and European continents are drifting apart at an…

A: The drift is 3 cm in 1 year. For 1 cm(=10-2m ) ,the time taken is t0=13  year For 1 m drift ,the…

Q: For a short time, the speed v of a car, in m / s, is given by v = at2 + bt3, where t is the time in…

A:

Q: How many minutes Raman will take to cover a distance of 400 meters if he runs at a speed of 20 km/hr…

A:

Q: A body travels uniformly a distance of (13.8+0.2) m in a time (4.0 + 0.3) S. The velocity of the…

A: Correct option (b) (3.45±0.3) m/s

Q: The position of an object moving along a line at any time t 2 0 is given by the function s(t) = t³ –…

A: The position of an object  is given by,s(t)=t3-9t2+18........ t≥0......(1)where, s(t) is in feets…

Q: The deck of a bridge is suspended 225 feet above a river. If a pebble falls off the side of the…

A: Please see the answer below

Q: A body moving with uniform acceleration has a velocity of 11.5 cm/s when its X coordinate is 5.0 cm.…

A: u = 11.5 cm/s  Xi = 5 cm  Xf = - 5 cm  Time is t = 6 s .

Q: The function s = f(t) gives the position of a body moving on a coordinate line, with s in meters and…

A:

Q: The velocity V of a small vèhicle was measured, starting from rest. t (s): 0.0 2.5 5.0 7.5 10 V 0.00…

A: Velocity: Velocity is defined as the rate of change of displacement of a body with respect to time.…

Q: A particle moves according to a law of motion s = f(t) = t - 15t2 + 72t, tz 0, where t is measured…

A: We have position of the particle given by s=t3-15t2+72t, velocity of the particle v=3t2-30t+72 and…

Q: The x component of the velocity of an object moving along the x axis is given as vy = 4t – 3t where…

A:

Q: If s (t) = 4t3 – 3t describes the position of a particle moving along a straight path where s (t) is…

A:

Q: The speed v ms-' of a particle moving in a straight course at time t seconds is v = 9t2 – 8t – 6.…

A:

Q: MHE Reader B Tin (Sn) exists in QUESTION 3 A camel walks 8.09 km North, then 12.2 km East, and…

A:

Q: A physics student with a stopwatch drops a rock into a very deep well, and measures the time between…

A: Given: The speed of the sound is 343 m/s. The total time is 6.2 s. The initial speed of the stone is…

Distance and Speed

The speed, distance and time relation forms the basis of study of motion. You will need these concepts in the study of Mechanics. This concept is applicable for students who are studying the following courses –