Contextual Applications of Differentiation

Given that an object’s acceleration along a line is defined by $a(t) = -8e^{0.t}$ and starts from rest, which expression defines its initial velocity after seconds?

A working ant moves in a straight line with its velocity function given by $v(t) = t^2 - 3t + 2$. During which time intervals is the ant moving to the right?

A particle moves along a line so that its displacement from its starting point after t seconds is given by the equation $x(t)=\frac{1}{4} t^{4}-\frac{1}{2} t^{2}$; how many times during the motion can it be guaranteed to have returned to its starting speed based on Mean Value Theorem?

On a graph representing straight-line motion, what does a horizontal line signify?

If the position of a particle is given by $s(t) = t^3 - 6t^2 + 9t + 4$, at what time $t$ does the particle change direction?

A soccer player kicks a ball in a straight line. The position of the ball as a function of time is given by $s(t) = t^2 - 3t + 1$. What is $a(t)$, the acceleration of the ball as a function of time?

A car's position on a straight track can be modeled by the equation $s(t) = 5\cos\left(\frac{\pi}{6} t\right)$. What represents the car's speed at any time $t$?

What does the derivative of a position function at a specific point represent?

What is the slope of the line represented by the equation $y = 3x + 4$?

A ball thrown vertically upwards follows the height-time relationship $h(T) = 250T - 20T^2$ where $T$ is in seconds. What will be the maximum height attained by the ball?