Question

The acceleration of a particle is increasing linearly with time t as βt. If the particle starts from origin with initial velocity u, the distance travelled by it in t second is

• A. ut + 1/2 βt³
• B. ut + 1/4 βt³
• C. ut + 1/3 βt³
• D. ut + βt³/6

Answer 1

Answer: (D)

ut + βt³/6

Answer 2

Using the relation,

S = ut + $\frac{k}{(n + 1)(n + 2)}t^{n + 2}$

For non – uniform accelerated motion, we get

S = ut + $\frac{\beta}{(1 + 1)(1 + 2)}t^{1 + 2}$

(There a = βt so comparing it with a = ktⁿ we get n = 1)

∴ S = ut + βt³/6