91Ó°ÊÓ

Memory. In a memory experiment, the rate at which students memorize Spanish vocabulary is found to be given by $$M^{\prime}(t)=0.2 t-0.003 t^{2}$$ where \(M(t)\) is the number of words memorized in \(t\) minutes. a) Find \(M(t)\) if it is known that \(M(0)=0\) b) How many words are memorized in 8 min?

Distance and speed. A motorcycle accelerates at a constant rate from 0 mph \((v(0)=0 \text { ) to } 60 \text { mph in } 15\) sec. a) How fast is it traveling after 15 sec? b) How far has it traveled after 15 sec? (Hint: Convert seconds to hours.)

Distance and speed. A car accelerates at a constant rate from 0 mph to 60 mph in 30 sec. a) How fast is it traveling after 30 sec? b) How far has it traveled after 30 sec?

Distance and speed. A cheetah decelerates at a constant rate from \(50 \mathrm{km} / \mathrm{hr}\) to a complete stop in \(20 \mathrm{sec}\). a) How fast is the chectah moving after 10 sec? b) How far has the cheetah traveled after \(20 \mathrm{sec} ?\)

Distance. For a freely falling object, \(a(t)=-32 \mathrm{ft} / \mathrm{sec}^{2}\) \(v(0)=\) initial velocity \(=v_{0}(\text { in } \mathrm{ft} / \mathrm{sec}),\) and \(s(0)=\) initial height \(=s_{0}(\text { in }[t) .\) Find a general expression \(\operatorname{lor} s(t)\) in terms of \(v_{0}\) and \(s_{0}\)

Evaluate. $$\int_{-2}^{2} \sqrt{4-x^{2}} d x$$