Question

The displacement of a car during its journey is given by s = xt² - yt + z where x, y and z are constants and t is the time. The acceleration of the car at t = 4 s is
1. 4 m/s²
2. 2x 
3. √2 kmph
4. None of the above

Answer 1

Correct Answer - Option 2 : 2x 

The correct answer is option 2) i.e. 2x units

CONCEPT:

• Velocity: The rate of change in displacement is called velocity.
• Acceleration: The rate of change in velocity is called acceleration.

Let the displacement of a particle be x.

Velocity, v	\(\frac{dx}{dt}\)
Acceleration, a	\(\frac{dv}{dt}\)

CALCULATION:

Given that: Displacement , s = xt2 - yt + z

• The velocity of the car, 

\(\Rightarrow v = \frac{ds}{dt} = \frac{d(xt^2 -yt + z)}{dt}= 2xt - y\)

• Acceleration of the car, 

\(\Rightarrow a = \frac{dv}{dt} = \frac{d(2xt - y)}{dt} = 2x\)

• The acceleration of the car is time-independent and therefore, at any instant, the acceleration will be 2x.