Question

Given a = 2t+5. Calculate the velocity of the body after 5 sec. If it starts from rest.

[a] 50 m/s [b] 25 m/s [c] 100 m/s [d] 75 m/s​

Answer 1

Answer:

(d) 75 m/s²

Explanation:

Time (t) = 5 sec.

Acceleration (a) = 2t+5 = 2×5+5 = 10+5 = 15m/s².

Initial velocity (u) = 0 {Because,it starts from rest}

Final velocity (v) = ?

v = u + at

v = 0+ 15 × 5

v = 75 m/s

HENCE, THE VELOCITY IS 75 M/S².

Answer 2

Given info : acceleration of a body varies with time as , a = 2t + 5 .

To find : the velocity of the body after 5 sec is ...

solution : initial velocity of the body, u = 0 m/s

acceleration , a = 2t + 5

we know, acceleration is the rate of change of velocity with respect to time.

⇒ a = $\frac{dv}{dt}$

⇒ ∫a dt = ∫ dv

⇒ $\int\limits^5_0{(2t+5)}dt=\int\limits^v_u{dv}$

⇒ $\left[t^2+5t\right]^5_0=v-u$

⇒ 5² + 5 × 5 = v - 0

⇒ 50 = v

⇒ v = 50 m/s

therefore the velocity of the body after 5 sec is 50 m/s . so the correct option is (a) 50 m/s.