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: The acceleration of an object (in m/s?) is given by the function a(t) = 4 sin(t). The initial…

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Q: The coordinate of an objec is given as a function of time by.x(1)=7t-3t2, where in meter and t in…

A: Given, Position, x(t)=7t-3t2

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: Tectonic plates are large segments of the Earth's crust that move slowly. Suppose that one such…

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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: 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: You are driving home from school steadily at 97 km/hkm/h for 160 kmkm . It then begins to rain and…

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Q: the motion of the particle is described by the equation x(t)=at^3-bt^2. where a is 3.36 in m/s^3 and…

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Q: You are exploring a planet and drop a small rock from the edge of a cliff. In coordinates where the…

A: we have to understand the graph.

Q: An object's position in the x-direction as a function of time is given by the expression; x(t)- 5t²…

A: Given data:  The position function of the object x = 5t2 + 2t Required: The average velocity between…

Q: A car starts moving at 60 mi/hr. After some time, the car speed reduces to 40 mi/hr and stays there…

A: Let's denote the time the car moved at 60 mi/hr as t (in hours). Then, the time the car moved at 40…

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: 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: The polynomial -5.041x2+2.382x-0.004 (from Ax2+Bx+C) is used to represent the verticle position (m)…

A: In an expression each term on addition must possess same unit.

Q: An adventure racer ran 1.7 km north, then 3.2 km 63° to the south of due east, then 1.4 km west. She…

A: Answer..

Q: Figure 1 shows the velocity-time graph of a person moving along one straight path called the x-axis.…

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Q: The coordinate of an object is given as a function of time by x = 7t - 3t2, where x is in meters and…

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Q: The displacement of a particle is given by s= 5t³ - 59t² + 87t-68 where s is in feet and t is in…

A: First we find expression  for velocity  and acceleration then after putting value of t as required…

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: The velocity of a particle is given by the function v(t)=t^2-7t+1027 , where the velocity is…

A: Given Data : The function of velocity is given as vt=t2-7t+10 The displacement of the particle in…

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: A kicker kicks a football upward from the ground at an initial velocity of 63 feet per second. The…

A: Given: u=63ft/s, d=70ft (a) The trajectory of the football is found by : h=ut+12gt2 At the highest…

Q: As you are driving to school one day, you pass a construction site of a new building and you stop to…

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Q: A car has acceleration of 4 m/s2 and starts from 1.8 m/s. What is its speed after 7.4 seconds, in…

A: Given acceleration a=4m/s2Initial speed u=1.8mstime t=7.4 s

Q: The velocity of a car is given by the following graph/function: v(t) v(t) = 1.5+0.8t – 0.01t³ Where…

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Q: What is the sum, expressed in the correct number of significant figures, of the measured values 21.4…

A: The objective of the question is to find the sum of the given measurements and express it in the…

Q: What is the acceleration of the object at t = 2.5 s? (Indicate the direction with the sign of your…

A: Given data: Initial velocity (Vi) = 10 m/s at t = 1 s Final velocity (Vf) = 2 m/s at t = 4 s…

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: The displacement of a particle is given by s= 2t3-42t² + 120t - 68 where s is in feet and t is in…

A: Given that: The displacement of the particle is s = 2t3-42t2+120t-68 The time is given as: t1=3.3…

Q: An object's position in the as a function of time obeys the equation; x (t) = 3t – 2t³ + 1.5t where…

A: Given displacement as function of time  Velocity is rate of change of displacement . Therefore…

Q: Assume your hair grows at a rate of 1/44th of an inch per day. How fast is that in nm/s (nanometers…

A: Relation between units of length: 1 inch =2.54×107 nm units of time: 1 day=24×3600 s Grow rate of…

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: An object's position in the  as a function of time obeys the equation;  x(t) = 14.2/t2.17 + 5.1t3…

A: x(t) = 14.2/t2.17 + 5.1t3 = 14.2t-2.17 + 5.1t3 t = 1.93 s v = ?

Q: A space shuttle is fired and the position of the shuttle is given by r(t)=(2*t*t-5*t)i+…

A: The position is given as: rt=2t2-5ti^+3t+1j^+12t3k^   The velocity is given as :…

Q: An object's position as a function of time in one dimension is given by the expression; 3.8t2 + 2.3t…

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Q: Amel goes for a walk with a speed of 3kph. After 30 minutes of walk, his wife follows him. Walking…

A: Given:  speed of Amel vA=3Kphtime gap between Amel and his wife = 30min =0.5 hrdistance travel by…

Q: If an average-size man jumps from an airplane with an open parachute, his downward velocity t…

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Q: Tom Cogwagee Longboat, of the Six Nations of the Grand River, is one of Ontario's best known…

A: Given: Distance=39.2 kmTime=2hours, 24min, 24sec

Q: Suppose your hair grows at the rate of 1/34 inch per day. Find the rate at which it grows in…

A: Given Data: The rate of hair growth is: r=1/34 inch/day

Q: A piece of wood moves at a velocity (measured in millimeters per year) of v(1) = r² – 3t – 4 where 1…

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Q: 4. A computer animator is trying to make an animation of a rabbit rushing back and forth along a…

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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 –