If f(t)=−t2+5t+3 describes the distance that a ball has travelled in meters, what is the instantaneous rate of change of the ball at one second?

Q: A space probe on the surface of Mars sends a radio signal back to the Earth, a distance of…

A: Given data: The distance between Mars and Earth d = 7.86×107 km speed of light v =3×108 m/s

Q: Position (cm) Elapsed Time (ms) 0. 0. 20 237 40 325 60 409 80 469 520 100

A: The positive X-axis represents the position and the positive Y-axis represents the elapsed time. The…

Q: The displacement of a particle is given by s = 4t3-70t2 + 112t-34 where s is in feet and t is in…

A: Given: s=4t3-70t2+112t-34 ft

Q: An object's position as a func of time is given by ; x(t) = - 200 (( t + 1 ) ^ - 1) + 6t^2.  (Assume…

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Q: The v -t graph for the motion of a car as it moves along a straight road is shown. When t-0, a-0.…

A: Velocity is defined as the rate of change of displacement. Thus, the displacement can be found by…

Q: In an airport moving walkways help get passengers to their gates faster. In one case a person stands…

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Q: Shown below is a graph of velocity versus time for a moving object. The object starts at position x…

A: Given Data:  Initial position of object x=0 m Final time t=2 s At t=2 s, velocity (v)= 10 ms

Q: A spaceship is traveling at a velocity of v0 = (37.3 m/s)i when its rockets fire, giving it an…

A: Data Given ,  Initial velocity ( V0 ) = ( 37.3 i ) m/s Acceleration ( a ) = ( 2.55 i + 4.19 k ) m/s2…

Q: The men's world record for swimming 1500.0 m in a long course pool (as of 2007) is 14 min 34.56 s.…

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Q: Question 2: Answer the following questions based on the graph given below Length vs Time^2 5 4.5 4…

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Q: At time t = 0 s, an object is observed at x = 0 m; and its position along the x axis follows this…

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Q: A block is moving along the x-axis and its position varies in time according to the expression x =…

A: Given: x = 3.00 m/s2t2 a Position at t = 3.20 sxat t=3.20 = 33.202∴xat t=3.20 = 30.72 m

Q: How much distance does he travel ?

A: Given data; Speed of men=20 ms-1Time taken by him=60 minFind distance does he travel ?

Q: A car goes from point A to point B. The speed of the car is constant at 88 km/hr for 65% of the…

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Q: An object's position can be modeled with the following function: s(t) = 2cos(2πt) +t^2, where t is…

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Q: Use the definition of the derivative to find an expression for the instantaneous acceleration of an…

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Q: A nerve impulse travels along a myelinated neuron at 60.3 m/s. What is this speed in mi/h and What…

A: Given in question - Speed of neuron (v) = 60.3 m/s To find - What is this speed in mi/h and What is…

Q: Why is it km and not meters, if c = 3x10^8 m and G has meter in the constant

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Q: n object's velocity as a function of time in one dimension is given by the expression; v(t) = 2.71t…

A: Object's velocity as a function of time is Find:Object's velocity at time

Q: space probe on the surface of Mars sends a radio signal back to the Earth, a distance of 9.86 ✕ 107…

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Q: A rocket ship has a position given by x(t)=bt2 meters. In order for it to reach a velocity of 5,000…

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Q: Suppose we measure a car's velocity every two seconds and obtain the data in the table: time(sec) 0…

A: S.No Time(s) Velocity (ft/s) Velocity (m/s) 1) 0 10  3.048 2) 2 28 8.5344 3) 4 42 12.80 4) 6…

Q: As your friend skateboards down a hill, you measure their velocity at 1.0-second intervals. You…

A: Given data:  Initial velocity at t = 0.0 s u = 0.0 m/s Final velocity at t = 2.0 s v = 4.6 m/s…

Q: An object's position as a func of time is given by ; x(t) = - 200 (( t + 1 ) ^ - 1) + 6t^2.  (Assume…

A: Given,x(t) = -200 ((t+1)-1)+6t2t = 3 s

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

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Q: x (m) Position as a function of time t = 4.00 s 40 20 (s) 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6…

A: Position time, velocity time and acceleration time graph are given.

Q: A box is moving along the x-axis and its position varies in time according to the expression x =…

A: Given that:- Postion of box varies with time.

Q: By looking at the figures given below, obtain the vectors given in the options and in terms of…

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Q: t time t seconds, the velocity (in m/s) of a bead sliding on a wire is given by the equation:…

A: Given: Velocity at time t is given by: v(t) = 4t3 - 3t2

Q: An Olympic bobsled goes 41 m in 2.6 s. How fast was it travelling in m/s? Be sure to answer with the…

A: Speed is given by V = distance/time

Q: Alice is riding a bike at 12 mph, but decides to sprint.  She takes 0.7 s to accelerate to 19 mph.…

A: Acceleration defined as a rate of change of velocity. Acceleration is a vector quantity, because it…

Q: The Tokaido Shinkansen high-speed trains often operate at a speed of 320 km/hr. Calculate the…

A: Speed, v = 320 km/hr  1 km/hr = 11.609miles/hr

Q: Given the quantities a = 6.7 m, b = 3.1 s, c = 80 m/s, what is the value of the quantity d = cb² ?

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Q: A car starting from rest is accelerated for 1 m/s2 for (5+5) seconds. It continues at constant…

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Q: A car can accelerate from 0 to 60 miles per hour in 3.2 s. What is its average acceleration, in…

A: Given : vi = 0 miles per hour = 0 m/s vf = 60 miles per hour = 26.8224 m/s dt = 3.2 s

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 –