Question

A particle is moving such that its displacement at any time t is
given by s = 2t3
– 5t2
+ 4t-3. Here s is in m and t is in seconds.
Find the time when the acceleration of particle is 14ms-2
.

Answer 1

Explanation:

s=t

3

−6t

2

+3t=4

v=

dt

ds

=3t

2

−12t+3

a=

dt

dv

=6t−12

So, acceleration will be zero at

6t−12=0

t=2sec

Then velocity at t = 3

v=3(2)

2

−12(2)+3

= 12-24+3

v=−9m/s

Answer 2

Answer:

Given : s = 2t³-5t²+4t-3

Now,

ds/dt = v = d/dt (2t³-5t2+4t-3)

= 2(3t³)-5(2t)+4+0

= 6t²-10t+4

Now,

a = dv/dt = d/dt ( 6t²-10t+4)

= 12t-10

Given that a = 14m/s² , t=?

Now,

a = 12t - 10

14 = 12t - 10

14+10 = 12t

12t = 24

t = 24/12

t = 2 second

HOPE IT HELPS YOU