Specialist2025 NHT Exam 1 · Q7Tech-free6 marks

Toy car with piecewise constant acceleration

A toy car travels along a straight, horizontal track.

At time $t = 0$ seconds, the toy car starts from rest at line $O$ and accelerates with positive constant acceleration until it reaches a velocity of $10 \text{ m s}^{-1}$ .

It then undergoes a constant acceleration of $- 4 {m s}^{- 2}$ until it attains a velocity, , of .

Sketch the velocity-time graph of the toy car on the axes below.

Blank velocity-time axes with v from -2 to 10 marked in steps of 2, origin O, and a point t_F marked on the t-axis.

1 mark

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b.i.

The acceleration of the toy car is positive for twice the amount of time that the acceleration of the toy car is negative.

Show that it takes 9 seconds for the toy car to reach line $F$ from line $O$ .

1 mark

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b.ii.

Show that the equation for the velocity of the toy car when it has negative acceleration is given by $v = 26 - 4t$ .

1 mark

Hints, answer checking and worked solutions come with a Season Pass.