Question

Q7.The displacement of the body x(in meters) varies with time t (in sec) as x=−2t/3t2+16t+2 find following what will the displacement when it comes to rest

Answer 1

Correct Question

The displacement of the body x(in meters) varies with time t (in sec) as x=−2t²/3+16t+2 find following what will the time when it comes to rest.

Solution -

Displacement i.e. x of the body varies with time i.e. t.

x = -2t²/3 + 16t + 2

Velocity = Displacement/Time

v = ds/dt { Here, s = X }

v = dx/dt

v = d(-2t²/3 + 16t + 2)/dt

v = -2*2t + 16

v = -4t + 16 ............(1st equation)

We have to find the time taken by the body body when it (body) comes to rest. When body comes to rest. Then velocity become zero.

So, substitute value of v = 0 in (1st equation)

0 = -4t + 16

4t = 16

Divide by 4 on both sides,

4t/4 = 16/4

t = 4

Given in question that, time i.e. t is in seconds.

Therefore, the time taken by the body is 4 sec.

Additional Information

Velocity = (Change in position)/(Change in time) = ds/dt

Acceleration = (Change in velocity)/(Change in time) = dv/dt

Velocity is a vector quantity as it has both magnitude and direction.

S.I. unit of velocity is m/s.

Dimensional formula of velocity = [L]/[T] = [L¹T-¹]

Answer 2

CORRECT QUESTION:

The displacement of the body is x m varies with time t s as x = -2t²/3 + 16t + 2 . Find following what will the displacement when it it come to rest

GIVEN:

• Distance ( s ) = x m
• Time ( t ) = t s

TO FIND:

• Displacement when it comes rest.

SOLUTION:

Given , x = -2t²/3 + 16t + 2

Velocity = Displacement/Time

Velocity = ds/dt

Here, s = x

Velocity = dx/dt

Substituting value of x

Velocity = d(-2t²/3 + 16t + 2)/dt

Velocity = -4t + 16

Assuming as equation 1

Now, substituting v = 0 in equation 1

→ 0 = -4t + 16

→ 4t = 16

→ t = 16/4

→ t = 4s ( Answer )

.°. Time taken by the body is 4s