Question

The velocity of a particle moving with a uniform acceleration of 10 ms-2 after 5 s is 50 ms. Its velocity
at t=4 s is
a) 10 ms-1
b) 20 ms-1
c) 30 ms-1
d) 40 ms-1
​

Answer 1

$\Large\boxed{\sf{\quad(d)\quad\!40\ m\ s^{-1}\quad}}$

The particle moves with uniform acceleration of $\sf{10\ m\ s^{-2}.}$

• $\sf{a=10\ m\ s^{-2}}$

The particle attains a velocity of $\sf{50\ m\ s^{-1}}$ at a time $\sf{t=5\ s.}$

$\longrightarrow\sf{v(5)=50}$

By first equation of motion,

$\longrightarrow\sf{u+at=50}$

$\longrightarrow\sf{u+10\times5=50}$

$\longrightarrow\sf{u+50=50}$

$\longrightarrow\sf{u=0}$

So the particle started its journey from rest.

Well, the velocity as a function in time $\sf{t}$ is, by first equation of motion,

$\longrightarrow\sf{v(t)=10t}$

So at t = 4 seconds,

$\longrightarrow\sf{v(4)=10\times4}$

$\longrightarrow\sf{\underline{\underline{v(4)=40\ m\ s^{-1}}}}$

Hence $\sf{(d)\ 40\ m\ s^{-1}}$ is the answer.