Question

A model car is moving around a circular track of radius 3.0 m at a speed of 1.5 m s⁻¹ as shown in the figure. It takes the car 12.6 s to complete one full lap.

What is the magnitude of the average acceleration of the car (a) between point A and point B? (in m s⁻² to 2 s.f)

Answer 1

Solution.

$R=3.0m;$

$v=1.5ms^{-1};$

$T=12.6s;$

$a_{average}-?;$

$a_{average}=\frac{\Delta\upsilon}{\Delta\tau};$

$\Delta\upsilon=\sqrt{\upsilon^2+\upsilon^2}=\sqrt{2\upsilon^2};$

$\Delta\upsilon=\sqrt{4.5}=2.12ms^{-1};$

$\Delta\tau=\frac{T}{4};$

$\Delta\tau=\frac{12.6}{4}=3.15s;$

$a_{average}=\dfrac{2.12ms^{-1}}{3.15s}=0.67ms^{-2};$

Answer: $a_{average}=0.67ms^{-2}.$