Question

The position of a particle is given by x = 5t2 + 2t + 5. What is the acceleration of the particle at t = 1 sec?
1. 10 m/s²
2. 12 m/s2
3. 25 m/s2
4. 7 m/s2

Answer 1

Correct Answer - Option 1 : 10 m/s²

CONCEPT:

• Velocity: The displacement per unit time is called velocity.

\(v = {Δ x \over Δ t}\)

where v is the velocity, Δx is the change in displacement, Δt is the change in time.

• Acceleration (a): The rate of change of velocity is known as acceleration.
  • It is a vector quantity.

\(\overrightarrow{a} = {\overrightarrow{Δ v} \over Δ t} \)

where a is the vector quantity, Δv is the velocity, and Δt is the time.

CALCULATION:

Given that position of a particle is given by: x = 5t2 + 2t + 5

velocity \(v = {Δ x \over Δ t}\)

\(v = {d x \over d t}={d \over d t}(5t^2 + 2t + 5) = 10t+2\)

​\(\overrightarrow{a} = {\overrightarrow{Δ v} \over Δ t} = {d(10t+2) \over d t} =10 m/s^2\)

So the correct answer is option 1.