Question

(a) Explain the meaning of the following equation of motion :
v = u + at
where symbols have their usual meanings

(b) A body starting from rest travels with uniform acceleration. If it travels 100 m in 5 s, what is the value of acceleration?

Answer 1

(a) The given equation is the first equation of motion i.e.,
v = u + at
Where,
(a) - Acceleration
(v) - Final velocity
(u) - Initial velocity
(t) - Time taken
It gives the velocity acquired by a body in time t provided initial velocity and acceleration is known.

(b) We have to find the acceleration of the body. We have the following information given, Initial velocity,
Let the acceleration be (a)
Time taken,(t) = 5 s
Distance travelled, (s) = 100 m
We can calculate the distance travelled by using the 2^nd equation of motion,
$s=ut+\frac{1}{2}a{t}^2$
Put the values in above equation to find the acceleration of the body,
$100=0\left(5\right)+\frac{1}{2}\left(a\right)\left(5^2\right)$
On further simplification,
$\frac{25a}{2}=100$
Therefore,
$$\begin{gathered} a=\frac{200}{25} \\ =\boxed{8\mathrm{m}/{\mathrm{s}}^2} \end{gathered}$$