Physics

Problem

A trolley moves along a straight track and its velocity is recorded every

2\,\text{s}

as follows: Time

t

(s):

\;0 \quad 2 \quad 4 \quad 6 \quad 8

Velocity

v

(

m\,\text{s}^{-1}

\;0 \quad 6 \quad 10 \quad 12 \quad 13

a. (i) Plot the velocity–time graph by joining the points with a smooth curve. b. (ii) By drawing a suitable tangent, estimate the instantaneous acceleration at

t=3\,\text{s}

. c. (iii) Use a graphical method (such as counting squares or dividing the area into convenient geometrical shapes) to find the displacement of the trolley in the first

8\,\text{s}

. d. (iv) Calculate the average acceleration for the interval

0

–

8\,\text{s}

and comment on its sign.

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