Question

A model car company produces battery-powered model cars. At its maximum
acceleration, their latest model accelerates from rest to its top speed in 3.5 s.
a) While the car is travelling at its top speed, it covers 180 m in 9.0 s.
Calculate the car's maximum acceleration.
b) Calculate how fast the car would be moving if it accelerated from rest for 1.5 seconds
with its maximum acceleration.

Answer 1

Answer:

a) 5.714 m/s²

b) 13.33 m/s²

Explanation:

, $\text{The final velocity, }\text{\ensuremath{v_{f}}}\text{ of the car is }\text{\ensuremath{\dfrac{\Delta v}{\Delta t}=}}\dfrac{{180m}}{9.0s}=20\;m/s$

The car goes from an initial velocity of 0 m/s  to this final velocity in t=3.5s

Therefore the acceleration of the car is given by
$\displaystyle a=\boldsymbol{\dfrac{{v}_{f}-{v}_{0}}{t}}$

where $v_0$ is the initial velocity

$a=\dfrac{20-0}{3.5}=\dfrac{20}{3.5}=5.714\mathrm{m/s^{2}}$

Part a
$\text{Maximum\;Acceleration}}}=5.714 \;m/s^{2}$

Part b)

If the car accelerated from rest and reached final speed of 20 m/s in 1.5s instead of 3.5s then

$a=\dfrac{\boldsymbol{20}}{\boldsymbol{1.5}}={\displaystyle \textbf{13.33}\;m/s^{2}}$