Question

Starting from a stationary position, Rahul paddles his bicycle to attain a velocity of 6 $m{s^{ - 1}}$ in 30sec. Then he applies brakes such that the velocity of the bicycle comes down to $4m{s^{ - 1}}$ in the next 5 sec. calculate the acceleration of the bicycle in both the cases.

Answer 1

Hint – In this question use the first equation of motion that is $v = u + at$, the initial velocity of Rahul is zero, use this to calculate the value of acceleration in the first case, now after applying brakes the final velocity reduces to $4m{s^{ - 1}}$ whereas the initial velocity will the final velocity of the previous case. This will get the value of acceleration in both the cases.
Formula used –
As we know the first equation of motion which is given as:
$v = u + at$........................ (1),
where u = initial velocity
            v = final velocity
            a = acceleration
            t = time.
Complete step-by-step solution -
Now in the first case, Rahul paddles from the starting point so his initial velocity is zero and attains a velocity of 6 m/s in 30 sec.
Therefore his final velocity is 6 m/s and he takes time 30 sec.
So from equation (1) substitute the values we have,
$ \Rightarrow 6 = 0 + a\left( {30} \right)$
$ \Rightarrow a = \dfrac{6}{{30}} = 0.2m{s^{-2}}$.
So in the first case his acceleration is $0.2m{s^{-2}}$ .
Now in the second case he applies brakes such that the velocity of the bicycle comes down to 4m/s in the next 5s.
So his initial velocity becomes 6 m/s and final velocity becomes 4 m/s and the time taken is 5s.
So substitute these values in equation (1) we have,
$ \Rightarrow 4 = 6 + a\left( 5 \right)$
$ \Rightarrow a = \dfrac{{4 - 6}}{5} = \dfrac{{ - 2}}{5} = - 0.4m{s^{-2}}$ (‘-’ sign indicates retardation).
So this is the required answer.

Note – The key concept here was the negative sign of acceleration, retardation is opposite of acceleration and it generally comes into play when the final velocity of an object is less than the initial velocity of the object in a path. Acceleration is itself a vector quantity as it has both direction as well as magnitude.