Constant acceleration (suvat) equationsAQA A-Level Maths: Subtopic test

1. 1
   A car travels in a straight line with constant acceleration. Over a $6$ s period its speed increases from $8$ m s$^{-1}$ to $20$ m s$^{-1}$.

   (a)

   Find the acceleration of the car.

   [1 mark]

   • A$0.5$ m s$^{-2}$
   • B$2$ m s$^{-2}$
   • C$4.67$ m s$^{-2}$
   • D$12$ m s$^{-2}$

   (b)

   Find the distance travelled by the car in the $6$ s.

   [1 mark]

   • A$72$ m
   • B$120$ m
   • C$168$ m
   • D$84$ m

   (c)

   Find the speed of the car when it has travelled $50$ m from the start of the $6$ s period.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A train slows down with constant deceleration along a straight track. It passes a signal at $30$ m s$^{-1}$ and comes to rest $450$ m beyond the signal.

   (a)

   Find the acceleration of the train.

   [1 mark]

   • A$-1$ m s$^{-2}$
   • B$-2$ m s$^{-2}$
   • C$-0.5$ m s$^{-2}$
   • D$+1$ m s$^{-2}$

   (b)

   How long does the train take to stop after passing the signal?

   [1 mark]

   • A$15$ s
   • B$60$ s
   • C$30$ s
   • D$480$ s

   (c)

   Find the speed of the train when it is $200$ m beyond the signal.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A particle moves in a straight line with constant acceleration $a$. At time $t=0$ its velocity is $u$. At time $t$ its velocity is $v$ and its displacement from its starting point is $s$.

   (a)

   Using the definition of acceleration and the fact that the average velocity is $\frac12(u+v)$ for constant acceleration, derive the formula $s=ut+\frac12at^2$.

   [3 marks]

   (b)

   Hence, or otherwise, derive the formula $v^2=u^2+2as$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Two cars, $A$ and $B$, travel in the same direction along a straight road. At time $t=0$, car $A$ passes a point $P$ with speed $10$ m s$^{-1}$ and constant acceleration $1.5$ m s$^{-2}$. At the same instant car $B$ starts from rest at $P$ with constant acceleration $2.5$ m s$^{-2}$.

   (a)

   (i) Write down an expression for the displacement from $P$ of each car at time $t$.
   (ii) Find the time at which $B$ overtakes $A$.
   (iii) Find the distance from $P$ at which this happens.

   [6 marks]

   (b)

   (i) Find the speed of each car at the instant that $B$ overtakes $A$.
   (ii) Find the time at which the two cars have equal speeds, and the distance between them at that time.

   [6 marks]

   Total for question 4: 12 marks

End of questions