Question

The graph shows the rate of change of speed of a train. How much distance the train will cover at 60 seconds if it is accelerating with 2 m/s2?

Answer 1

Answer:

6000 m.

Explanation:

From the graph, we observe that the initial velocity(u) of the train is = 40 m/s, as at time instant t=0, velocity is 40.

∴ Initial velocity(u) = 40 m/s.

  Acceleration(a) = 2 m/s².

  Time(t) = 60 s.

∴ Distance travelled(s) = ut + 0.5at² = 40×60+0.5×2×60² = 6000 m = 6 km (Ans.)

Answer 2

Given:

The graph shows the rate of change of speed of a train.

To find:

Distance travelled?

Solution:

First of all, we will use EQUATION OF KINEMATICS to solve this question.

• See the graph :

• Initial velocity = 40 m/s

• Final velocity = u + at = 40 + 2(60) = 160 m/s

Now, let displacement be d :

${v}^{2} = {u}^{2} + 2ad$

$\implies \: {160}^{2} = {40}^{2} + 2(2)d$

$\implies \: 4d = {160}^{2} - {40}^{2}$

$\implies \: 4d = (160 - 40)(160 + 40)$

$\implies \: 4d =200 \times 120$

$\implies \: d =200 \times 30$

$\implies \: d =6000 \: m$

$\implies \: d =6 \: km$

So, distance travelled is 6 km.