Question

The displacement of a particle moving along a straight line is given by x = 16t - 2t² . Find distance travelled after 2 and 6 seconds​

Answer 1

Step-by-step explanation:

The displacement is given by the equation,

x = 16t – 2t2

Displacement at t = 2 sec

x = 24 m

Displacement at t = 6 sec

x = 24 m

To calculate the distance we have to first find the velocity,

v = differentiation of (16t – 2t2)

v = 16 – 4t

Velocity become 0 at t = 4 sec

Distance travelled at t = 3 seconds

x = 30 m

Distance travelled at t = 6 seconds

x = 32 m

Answer 2

Step-by-step explanation:

Given:

x=16t−2t

2

Comparing with second equation of motion:

s=ut+

2

1

at

2

It can be concluded that:

u=16 m/s,a=4 m/s

2

Now, using first equation of motion:

v=u+at

v=16−4t

For v=0 we get, t=4s

Here, direction of velocity will reverse. So total distance travelled will be the sum of displacement in first four seconds and displacement in next four seconds.

Now,

Displacement at

t=0,x=0

t=4,x=32

t=8,x=0

∴ Distance = (distance from x=0 to x=32) + (distance from x=32 to x=0)

∴ Distance =32+32=64 m