The equation of motion of the particle is s=a t^2+b t+c . If the displacement after 1 second is 20 m , velocity after 2 seconds is 30 m / seconds and the acceleration is 10 ~m / seconds ^2 , then

Step-by-step solution

The displacement is given by s(t) = a t^2 + b t + c . The velocity is the derivative: v(t) = ds dt = 2a t + b , and the acceleration is A(t) = dv dt = 2a . Given A = 10 , it follows that 2a = 10 , so a = 5 . The velocity after 2 seconds is v(2) = 30 , so 2a 2 + b = 30 . Substituting a = 5 gives 20 + b = 30 , hence b = 10 . The displacement after 1 second is s(1) = 20 , so a + b + c = 20 . With a = 5 and b = 10 , this becomes 15 + c = 20 , yielding c = 5 . The option a + c = b evaluates to 5 + 5 = 10 , which is true