Key to Matching Game
Designed by Luke Tunstall
Justification – Here, because of the units and the look of the function, one can see that v(t) is some
version of sin(t). The derivative of sin(t) is cos(t), which must be our acceleration function, a(t).
Justification – This is a tricky one. In a similar manner to the function above, here our position function
is some version of sin(t). The associated velocity function must be some form of cos(t), and thus the
acceleration function must be sin(t), bringing us full circle.
Justification – Recall that speed is the absolute value (or magnitude) of velocity. Hence, we reflect the
velocity function about the x-axis, giving us the speed function.
Key to Matching Game
Designed by Luke Tunstall
Justification – The object here is constantly moving to the right, with the exception of a ‘rest’ in the
middle of the time period. Thus, we look for a velocity function that is always positive, while touching y
= 0 in the middle of the time period. From an algebraic perspective, this is confirmed in that the position
function appears to be cubic; as a result, the velocity function should be a quadratic.
Justification – This match is rather simple. The velocity has a constant, positive slope, so the
acceleration function should by a horizontal line above the x-axis.
Justification – Because the position function is a linear equation, this implies that the velocity function
must be a constant. Taking the derivative of a constant to get a(t), we get a(t) = 0.
Key to Matching Game
Designed by Luke Tunstall
Justification – For this position function, we note that the slope is both positive and steep as ‘t’ begins;
however, as ‘t’ increases, the slope levels off, and appears as though it will become horizontal. Thus, the
velocity function must be high and positive as ‘t’ begins, but begin approaching y = 0 as ‘t’ increases.
Justification – Here our velocity function appears to be quadratic. For the first half of the time period,
the slope is increasing. Then, the slope is zero for a moment, and begins decreasing for the last half of
the time period. The derivative of velocity, a(t), should thus begin positive, ‘touch’ zero, and be negative
for the remained of the time period.