Question

In a race, a runner traveled 12 meters in 4.0 seconds as she accelerated uniformly from rest. The magnitude of the acceleration of the runner was...

Answer 1

Use equation of motion
S = ut + 0.5at²

12 m = (0 m/s × 4.0 s) + (0.5 × a × (4.0 s)²)

a = 24/16 m/s² = 1.5 m/s²

∴ Acceleration of runner is 1.5 m/s²

Answer 2

Answer:  

The ‘magnitude of the acceleration’ of the runner was $\bold{1.5\ \mathrm{m} / \mathrm{s}^{2}}$.

Solution:

We know that the initial velocity is zero as the runner started from rest, the distance covered is given as 12 m and the time taken is 4 s.

The solution is to substitute the known values like, initial velocity, distance covered and time taken in the Newton’s second equation of motion to determine acceleration.

Newton’s second equation of motion is  

$s=u t+\frac{1}{2} a t^{2}$

Substitute s = 12 m, t = 4s and u = 0 in the above equation, we will get

$12=(0 \times 4)+\left(\frac{1}{2} \times a \times 4 \times 4\right)$

Thus, the acceleration will be  

$12=0+8 a$

$\Rightarrow 8 a=12$

$\Rightarrow a=\frac{12}{8}=1.5\ \mathrm{m} / \mathrm{s}^{2}$

Thus, the acceleration of the runner is $1.5\ \mathrm{m} / \mathrm{s}^{2}$.