Question

# The acceleration of a particle is increasing linearly with time t as bt. The particle starts from the origin with an initial velocity v0. The distance travelled by the particle in time t will be

A
v0t+13bt2
B
v0t+13bt3
C
v0t+16bt3
D
v0t+12bt2
Solution
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#### here it is given that a=btwkt, a=change in velocitychange in time=dvdt∴dvdt=bt now integrating this we will get vv=bt22+cAt t=0 s, v=v0, Thus v0=c∴v=bt22+v0Now. v=change in positionchange in time=dsdt=bt22+v0∴ds=(bt22+v0)dt∴ Integrating the above we get, s=bt36+v0t+c′at t=0, s=0∴c′=0i.e. s=bt36+v0t

16
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