Question

A car is travelling at a given instant 40 m/s on a circular road of radius 400 m. Its speed is increasing at the rate 3 m/s. Its acceleration is

• A. $4m/s^2$
• B. $3m/s^2$
• C. $5m/s^2$
• D. $2m/s^2$

Answer 1

The correct option is C $5m/s^2$

Given that,

Tangential acceleration $a_t=3m/s^2$

Velocity $v=40m/s$

Radius $r=400m$

We know that,

Centripetal acceleration is

$a_c=\frac{v^2}{r}$

$a_c=\frac{40\times 40}{400}$

$a_c=4m/s^2$

Now total acceleration is

$a=a_c+a_t$

$a=\sqrt{4^2+3^2}$

$a=5m/s^2$

Hence, the total acceleration is $5m/s^2$