A laboratory cart moves along a straight horizontal track

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

A laboratory cart moves along a straight horizontal track. Its acceleration as a function of time is described as follows: • From

t = 0

t = 2.0\,\text{s}

a_x = 2.0\,\text{m/s}^2

(positive). • From

t = 2.0\,\text{s}

t = 5.0\,\text{s}

a_x = 0

. • From

t = 5.0\,\text{s}

t = 8.0\,\text{s}

a_x = -1.5\,\text{m/s}^2

(negative). At

t = 0

the cart is at position

x = 0

and has a velocity of 1.0 m/s toward the

+x

direction. (a) Determine the cart’s velocity at

t = 2.0\,\text{s}

. (b) Determine the cart’s velocity at

t = 5.0\,\text{s}

. (c) Determine the cart’s velocity at

t = 8.0\,\text{s}

. (d) Calculate the cart’s displacement during each of the three time intervals and the total displacement from

t = 0

t = 8.0\,\text{s}

. (e) On axes provided in your answer booklet, sketch a qualitative graph of position

x

versus time for the interval

0 \le t \le 8.0\,\text{s}

, clearly indicating the curvature and slopes corresponding to your results.