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Question 1

Determine the displacement and total distance traveled by a particle moving with velocity $v(t) = 4\cos t - 2 \text{ m s}^{-1}$ over the interval $0 \le t \le \pi$ .

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Question 2

A particle travels with velocity $v(t) = (t - 3)^2 - 4 \text{ m s}^{-1}$ over the interval $0 \le t \le 6$ .

Find its displacement and total distance traveled.

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Question 3

Kinematics using calculus. Finding displacement and total distance from a velocity function.

A particle moves in a straight line with a velocity given by $v(t) = t^{2} - 8t + 12$ m s $^{-1}$ for $0 \le t \le 5$ .

Find the displacement of the particle and the total distance it travels in the first 5 seconds.

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Question 4

This question assesses the ability to calculate displacement and total distance traveled by a particle given its velocity function using definite integrals and absolute values.

For $0 \le t \le 3$ , a particle has velocity $v(t) = t^{2} - 4$ m/s. Find the displacement and the total distance traveled by the particle.

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Question 5

A particle's velocity $v$ in $\text{m s}^{-1}$ at time $t$ seconds is given by

v(t) = \begin{cases} 4, & 0 \le t \le 2 \\ -2, & 2 < t \le 5 \end{cases}

Find the particle's displacement and total distance traveled in the interval $0 \le t \le 5$ .

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Question 6

A particle moves in a straight line with a velocity function $v(t) = 5\text{ m s}^{-1}$ for $0 \le t \le 3\text{ s}$ .

1.

Find the displacement of the particle over this interval.

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2.

Find the total distance traveled by the particle over this interval.

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Question 7

Given $v(t) = t^{3} - 6t^{2} + 9t \text{ m s}^{-1}$ for $0 \le t \le 4$ , find the displacement and the total distance traveled.

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Question 8

Kinematics: calculating displacement and total distance by integrating a velocity function over a given time interval.

A particle moves with velocity $v(t) = 2t \text{ m/s}$ for $0 \le t \le 4 \text{ s}$ . Calculate the displacement and the total distance traveled.

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Question 9

A particle moves with velocity $v(t) = 4\cos(2t) \text{ m s}^{-1}$ for $0 \le t \le \pi$ . Find its displacement and the total distance traveled.

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Question 10

A particle moves along a straight line such that its velocity $v$ at time $t$ seconds is given by $v(t) = 3t^2 - 12t + 9$ , for $0 \le t \le 3$ .

Find the displacement and the total distance travelled by the particle.

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Question 11

A particle moves in a straight line such that its velocity $v$ at time $t$ seconds, for $0 \le t \le 2$ , is given by $v(t) = 10e^{-t} - 2 \text{ m/s}$ .

Compute the displacement and total distance traveled by the particle in this time interval.

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Question 12

A particle has velocity $v(t) = \sin t$ m/s for $0 \le t \le \pi$ . Determine its displacement and total distance traveled.

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Question Type 4: Accounting for the difference between distance and displacement Exercises