Question

a particle starts with initial velocity of 10ms-1 and moves with a uniform acceleration . It attains a velocity of 30ms-1 in 5 s . the time taken by the particle from here onwards to aquire a velocity of 60 ms-1

Answer 1

Here use the formula v=u+at

Answer 2

The time taken by the particle to acquire a velocity of 60m/s is 7.5sec.

Given:-

Initial velocity of particle = 10m/s

Final velocity of particle = 30m/s

Time taken = 5sec

Velocity after some time = 60m/s

To Find:-

The time taken by the particle to acquire a velocity of 60m/s.

Solution:-

We can easily find out the time taken by the particle to acquire a velocity of 60m/s. by using these simple steps.

As

Initial velocity of particle (u) = 10m/s

Final velocity of particle (v) = 30m/s

Time taken (t) = 5sec

Velocity after some time (v')= 60m/s

According to the formula of the first equation of motion,

$v = u + at$

Case 1

$v = u + at$

on putting the values,

$30 = 10 + a \times 5$

$30 - 10 = a \times 5$

$5 \times \: a = 20$

$a = \frac{20}{5}$

$a = 4$

Now, in the second case, the final velocity of a particle in the first case will be the initial velocity.

As

$v' =v + at$

$60 = 30 \times 4 \times t$

$60 - 30 = 4 \times t$

$4 \times t = 30$

$t = \frac{30}{4}$

$t = 7.5sec$

Hence, The time taken by the particle to acquire a velocity of 60m/s is 7.5sec.

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