Question

Two particles A and B starts from same point, A moves with constant velocity of 50 m/s and B starts from rest with constant acceleration of 10 m/s2, in same direction. After how much time, from the following, distance between them is 125 m?

Answer 1

$\Huge{\red{\underline{\textsf{Answer}}}}$

→ After 5 seconds the distance between them will be 125 m.

$\Huge{\red{\underline{\textsf{Solution}}}}$

→ Let after time t, the distance between them is 125 m.

Distance traveled by A in time

→ t = velocity × time

→d₁ = 50 × t

or, d₁ = 50t

♦ Since B starts from rest and with constant acceleration 10 m/s²

→Therefore, using second equation of motion

the distance traveled by B

→d₂ = $\dfrac{1}{2}$ × 10t²

or, d₂ = 5t²

Now,

d₁ - d₂ = 125

⇒ 50t - 5t²= 125

⇒ t² - 10t + 25 = 0

⇒ (t - 5)² = 0

⇒ t = 5

♦ Thus, after 5 seconds, the distance between them will be 125 m.

$\rule{200}2$