Question

Which of these equations/statements are true if acceleration is not constant?

• A. $s=ut+\left(\frac{1}{2}\right)a{t}^2$
  
• B. Displacement = Speed $\times$ Time
  
• C. The displacement traversed by an object is the area under its velocity – time graph
  
• D. $v=\frac{ds}{dt}$

Answer 1

Answer: (C), (D)

$v=\frac{ds}{dt}$

a. $s=ut+\frac{1}{2}a{t}^2$ is true for uniform acceleration motion. So, statement is false.
b. Distance = speed $\times$ time
displacement = velocity $\times$ time.
Speed and velocity are not interchangeable as one is a scalar and other is a vector which has a direction. So the statement is false.
c. Displacement traversed by an object is area under the velocity-time graph. This is true for any kind of motion irrespective of its acceleration. So the statement is true.
d. $v=\frac{ds}{dt},$ statement is true for all cases.