Question

$\huge\underline{\pink{\bf{Question:-}}}$
An object moves along the x-axis Its coordinates is given as function
of time as x = 7t - 3t² m where x is in metres and t is in seconds. Its average speed over the interval t =0 to t = 4 sec , is

a] 5 ms⁻¹

b] -5 ms⁻¹

c] $\sf{-\dfrac{169}{24}}$ ms⁻¹

d] $\sf{\dfrac{169}{24}}$ ms⁻¹



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Answer 1

11th/Physics

Kinematics (1D)

Answer :

Position of an moving object along x axis as function of time is given by

• x = 7t - 3t²

We have to find average speed of the object over the interval t = 0 to t = 4 second$.$

⧪ Average speed of body is defined as the ratio of total distance travelled to the total time taken.

It is a scalar quantity having only magnitude.

It can't be negative or zero (★)

Let's find total distance travelled by body!

• Position of body at different time :

at t = 0 : 7(0) - 3(0)² = 0 m

at t = 1 : 7(1) - 3(1)² = 4 m

at t = 2 : 7(2) - 3(2)² = 2 m

at t = 3 : 7(3) - 3(3)² = -6 m

at t = 4 : 7(4) - 3(4)² = -20 m

• Distance covered in intervals :

B/w 0 to 1s : |4 - 0| = 4m

B/w 1 to 2s : |2 - 4| = 2m

B/w 2 to 3s : |-6 - 2| = 8m

B/w 3 to 4s : |-20 - (-6)| = 14m

• Total distance travelled by body :

d = 4 + 2 + 8 + 14 = 28m

⧪ Average speed :

➙Vav = distance/time

➙ Vav = 28/4

➙ Vav = 7 m/s = 169/24 m/s

Cheers!

Answer 2

ANSWER:

Option d is the right answer.

SOLUTION:

Refer to the attachment

KEYS:

1.The differentiation of displacement gives velocity.

x = 7t - 3t²

V = dx/dt

V = 7 - 6t

Plot the velocity time graph using the above equation.

2.The velocity time graph and speed time graph are similar except negative part of velocity time graph.

3.The negative part of velocity time graph becomes positive in speed time graph.

4.The total area under speed time graph gives the total distance travelled.

5.Area under the graph upto t = 4 sec , gives the distance travelled upto 4 seconds.

From the graph ,

Total distance = 169/6 m.

Total time = 4 sec

6.Average speed = total distance / time taken.

Average speed = (169/6)(1/4)

Average speed = 169/24 m/s