Question

A body is moving in a circle with a speed of $1\text{m/s}$. This speed increases at a constant rate of $2\text{m/s}$ every second. Assume that the radius of the circle described is $25\text{m}$. The total acceleration of the body after $2\text{s}$ is

• A. $2{\text{m/s}}^2$
• B. $25{\text{m/s}}^2$
• C. $\sqrt{5}{\text{m/s}}^2$
• D. $\sqrt{7}{\text{m/s}}^2$

Answer 1

The correct option is C $\sqrt{5}{\text{m/s}}^2$

Let the tangential acceleration be $a_t$
and centripetal acceleration be $a_c$
$a_t=2{\text{m/s}}^2$
Then, velocity after $2\text{s}$ is
$v=u+a_{t}t=1+2\times 2=5\text{m/s}$

Centripetal acceleration at $t=2s$ is
$a_c=\frac{v^2}{r}=\frac{5^2}{25}=1{\text{m/s}}^2$

Hence, net acceleration
$=\sqrt{a_c^2+a_t^2}=\sqrt{1^2+2^2}=\sqrt{5}{\text{m/s}}^2$