Question

The position of a particle moving rectilinearly is given by x= t^3-3t^2-10.Find the distance travelled by the particle in first 4 second starting from t= 0

Answer 1

X = t^3-3t^2-10
differentiating b/s
=3t^2-6t
at t=4s
=3*4*4-6*4
=48-24
=24m
show the distance travelled by the particles in first 4 seconds starting from t=0 is 24m

Answer 2

Answer:

24m

Explanation:

x=t³-3t²−10

v=dx/dt =3t²−6t

Now, v=0 gives

t=0 and t=2sec

Velocity will becomes zero at t=2sec., so particle will change direction after t=2sec.

At t=0

x(0sec)=−10

At t=2sec

x(2sec)=(2)³−3(2)²−10 = 8−12−10 = −14

At t=4sec

x(4sec)=4³−3(4)²−10 = 64−48−10 = 6

Distance travelled =x1+x2

=|−14−(−10)|+|6−(−14)|=4+20=24

Distance Travelled =24 units.