Question

The displacement of a point moving along a straight line is given by
s = 4t2 + 5t-6
Here s is in cm and t is in seconds calculate
Initial speed of particle
(ii) Speed at t = 4s
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Answer 1

Question

The displacement of a point moving along a staright line given by:

s = 4t² + 5t - 6. Here s is in cm and t is in seconds. Calculate the -

(i) Initial speed of the particle

(ii) Speed at t = 4 sec

Solution -

Given, displacement is 4t² + 5t - 6 which is in cm and time is in seconds.

We have to find the initial speed of the particle and speed of the particle at t = 4 sec.

Now,

(i) Speed = Displacement/Time

Speed = ds/dt

Speed = d(4t² + 5t - 6)/dt

On solving we get,

Speed = 2*4t + 5

→ Speed = 8t + 5

As we have to find the speed of the particle from it's initial position. Initially it is at rest. So, at t = 0

Speed of particle = 8(0) + 5 = 0 + 5 = 5

Unit of displacement is cm and time is second (given).

Therefore, the initial speed of the particle is 5 cm/sec.

(ii) In second part we have to find the speed of the particle at t = 4 sec

On differentiation, we get

Speed of particle = 8t + 5 ....(1st equation)

[ Solved above ]

Now, substitute value of t = 4 in the (1st equation) to get the value of particle at t = 4 sec

Speed of particle = 8(4) + 5

= 32 + 5

= 37

Again unit of displacement is cm and time is second.

Therefore, the speed of the particle at t = 4 sec is 37 cm/sec.

Answer 2

Cᴏʀʀᴇᴄᴛ Qᴜᴇꜱᴛɪᴏɴ:

The displacement of apoint moving along a straight line is given by s = 4t² + 5t - 6

Here distance( s ) is in cm and time( t ) = 4s

Calculate:

( i ) Initial speed of particle

( ii ) Speed at t = 4s

Gɪᴠᴇɴ:

• Displacement = 4t² + 5t - 6 in cm

Tᴏ Fɪɴᴅ:

1. Initial speed
2. Speed at 4s

Sᴏʟᴜᴛɪᴏɴ ( i ):

Speed = Displacement/Time

Using differentiation

Speed = ds/dt

Substituting the value of s

Speed = d( 4t² + 5t - 6 )/dt

Speed = 2( 4t ) + 5

Speed = 8t + 5

As we have to find the initial speed . So, t = 0s

Substituting t = 0

Speed = 8(0) + 5

Speed = 5 cm/s

Hence , initial speed = 5cm/s

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Sᴏʟᴜᴛɪᴏɴ ( ii ):

Given

• time( t ) = 4s

Because we need to find the speed at the time of 4s

Speed = 8( t ) + 5

Substituting t = 4

→ Speed = 8(4) + 5

→ Speed = 32 + 5

→ Speed = 37 cm/s

Hence, speed of object at time of 4s = 37m/s