Laws of Motion — Question 13

We know that,

acceleration = $\dfrac{\text v - \text u}{\text t}$

Given,

m = 480 kg

u = 54 km h^-1

converting km h^-1 to m s^-1

$54 \text {km h}^{-1} = 54 \times (\dfrac{1000 \text {m}}{60 \times 60 \text {s}}) \\[0.5em] 54 \text {km h}^{-1} = 54 \times (\dfrac{10 \text {m}}{36 \text {s}}) \\[0.5em] 54 \text {km h}^{-1} = \dfrac{540 \text {m}}{36 \text {s}} \\[0.5em] 54 \text {km h}^{-1} = 15 {\text {m s}^{-1}} \\[0.5em]$

Hence, u = 15 m s^-1

v = 0

t = 10 s

Substituting the values in the formula above we get,

$\text a = \dfrac{0 - 15}{10} \\[0.5em] \Rightarrow \text a = -1.5\ \text{m s}^{-2} \\[0.5em]$

Hence, a = - 1.5 m s ^-2

The negative sign shows that it is retardation.

Now,

Force (f) = mass (m) x acceleration (a)

Substituting the values in the formula above we get,

$\text F = 480 \times (1.5) \\[0.5em] \Rightarrow \text F = 720\ \text N \\[0.5em]$

Hence,

Magnitude of force applied by the brakes = 720 N