The displacement and the increase in the velocity of a moving par… — Solution | JEE Physics

MCQEasyJEE 2024Motion in a Straight Line

The displacement and the increase in the velocity of a moving particle in the time interval from $t$ to $(t+1)$ seconds are $125 \, \text{m}$ and $50 \, \text{m/s}$ , respectively. The distance travelled by the particle in the $(t+2)$ th second is:

A
$100 \, \text{m}$
B
$150 \, \text{m}$
C
$175 \, \text{m}$
D
$200 \, \text{m}$

Answer

Correct answer:C

Step-by-step solution

Standard Method

Given: Displacement from $t$ to $(t+1)$ is $125 \, \text{m}$ and increase in velocity in this interval is $50 \, \text{m/s}$ .

Find: The distance travelled in the $(t+2)$ th second.

First find the acceleration. Since the time interval is $1 \, \text{s}$ ,

a = \frac{\Delta v}{\Delta t} = \frac{50}{1} = 50 \, \text{m/s}^2

Let the velocity at time $t$ be $u$ . Using displacement during the next $1 \, \text{s}$ ,

125 = u(1) + \frac{1}{2}(50)(1)^2

125 = u + 25

u = 100 \, \text{m/s}

Now the velocity at time $(t+1)$ is

u' = u + a(1) = 100 + 50 = 150 \, \text{m/s}

The distance travelled from $(t+1)$ to $(t+2)$ is

s = u'(1) + \frac{1}{2}(50)(1)^2

s = 150 + 25 = 175 \, \text{m}

Therefore, the distance travelled in the $(t+2)$ th second is $175 \, \text{m}$ . The correct option is C.

Common mistakes

Using the formula for displacement over many seconds without recognizing that the given $125 \, \text{m}$ is only for a $1 \, \text{s}$ interval from $t$ to $(t+1)$ . Treat this as motion during one second and apply the equation for that interval.
Confusing increase in velocity with velocity itself. The given $50 \, \text{m/s}$ is $\Delta v$ , not the initial velocity. First calculate acceleration using $a = \frac{\Delta v}{\Delta t}$ .
Taking the distance in the $(t+2)$ th second as the velocity at $(t+1)$ alone. Even in that one-second interval, acceleration still contributes through the term $\frac{1}{2}a(1)^2$ , so this term must be added.

Practice more Motion in a Straight Line questions

Get unlimited AI-adaptive practice, mastery tracking, and an AI tutor that explains every step — free to start.

Start free trial More on Motion in a Straight Line

Answer

Step-by-step solution

Common mistakes

Practice more Motion in a Straight Line questions

Related questions