Question

A particle O moves along a straight line and its position is given by x = t³ - 2t² + 2 [Where x is in meter and t is in seconds.] Velocity at t = 4 seconds is 
1. 33 m/s
2. 32 m/s
3. 34 m/s
4. 23 m/s

Answer 1

Correct Answer - Option 2 : 32 m/s

CONCEPT:

Velocity:

• The rate of change of displacement of an object (displacement over elapsed time) is velocity.
• Velocity is given by,

\(⇒ v = \frac{{dx}}{{dt}}\)

Acceleration:

• The rate of change of velocity is acceleration.
• Like velocity, acceleration is a vector and has both magnitude and direction.
• Acceleration is given by,

​\(⇒ a = \frac{{dv}}{{dt}}\)

CALCULATION:

Given:

The position of a particle as a function of time t (i.e., displacement) is x = t³- 2t² + 2 

• Now the velocity will be, 

\(⇒ v = \frac{{dx}}{{dt}} ⇒ v = 3t^2 - 4t\)

Now at t = 4sec,

The velocity will be,

⇒ v = 3 × 4² - 4 × 4 = 48 - 16 = 32 m/s

⇒ v = 32 m/s