Question

A ball bearing is placed on an inclined plane and begins to roll. The angle of elevation of the plane is θ. The distance (in meters) the ball bearing rolls in t seconds is s(t) = 4.9(sin θ)t2. (a) Determine the speed of the ball bearing after t seconds.

Answer 1

Answer:

Therefore  the velocity of the ball after t seconds is $9.8 sin\theta t$ m.

Step-by-step explanation:

Velocity: The ratio of distance to time.

Given that,

The distance the ball  bearing rolls in t seconds is

$S(t)=4.9 sin\theta t^2$

The first order derivative of distance of an object is the velocity of that object.

and the second order derivative of distance is acceleration.

$S(t)=4.9 sin\theta t^2$

Differentiating with respect of t

$\frac{d}{dt}S(t)=\frac{d}{dt}(4.9 sin\theta t^2)$

$\Rightarrow S'(t)= 4.9 sin\theta\frac{d}{dt}( t^2)$

$\Rightarrow S'(t)= 4.9 sin\theta(2t)$

$\Rightarrow S'(t)= 9.8 sin\theta t$

Therefore  the velocity of the ball after t seconds is $9.8 sin\theta t$ m.