Question

A ball is dropped from height at t=3s. What is instantaneous speed at t=18s and average speed at end of 20th second.(g=10m/s²)(s=gt)

Answer 1

Answer :-

• Instantaneous speed at t₁₈ = 10 m/s
• Average speed = 10 m/s

Given :-

◉ s = gt ; g = 10 m/s² ,

◉ A ball is dropped from height at t = 3s

To Find :-

◉ Instantaneous speed at, t = 18s

◉ Average speed at t = 20 s

Solution :-

First, We need to find the instantaneous speed at t = 18s

Given that,

⇒ s = gt [ Here, s = displacement ]

Differentiate both sides w.r.t t

⇒ ds/dt = d(gt) / dt

⇒ dv = g × dt/dt [ g is constant ]

⇒ dv = g

Hence, Instantaneous speed at t = 18 s would be 10 m/s. Or, At any time in the journey, The instantaneous would be same i.e., 10 m/s which indicates that the displacement time graph would be a straight line.

Also,

We need to find the average speed at t = 20 s

Given,

⇒ s = gt

Average speed is the slope of the chord drawn by the two points t = 0 s and t = 20 s,

But we need to find the change in displacement,

⇒ ∆s = g × 20 - g × 0

⇒ ∆s = 20×10

⇒ ∆s = 200 m

Time taken, t = 20 s [ ∆t = 20 ]

⇒ slope = ∆s / ∆t

⇒ slope = 200 / 20

⇒ slope = 10

Hence, Average speed would be 10 m/s.