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 + $\frac { \mathrm { k } } { ( \mathrm { n } + 1 ) ( \mathrm { n } + 2 ) } \mathrm { t } ^ { \mathrm { n } + 2 }$

For non – uniform accelerated motion, we get

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

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

∴ S = ut + βt³/6