Question

HELP PLEASE EASY MULTIPLE CHOICE!!! PPLLLLLLELEEEEEAAAASSSSSEEEE!!!!!

1.) If the velocity decreases, the acceleration has a _____ value.
Positive
Negative

2.) A car turns a corner at 15 kph. If the car were to turn in a shorter radius, the centripetal acceleration will _____ .
Decrease
Increase
If the radius of the arc is decreased to one-half, the centripetal acceleration is changed to _____ its original value.
1/2
1/4
2times
4times

Answer 1

1) The correct answer is negative.

In fact, in a uniform accelerated motion, the velocity at time t is given by
$v(t) = v_0 + at$
where v0 is the initial velocity, a is the acceleration and t the time. We see that if the velocity v(t) decreases, the acceleration a must be negative.
(in other words: when the acceleration is negative, it points against the direction of motion of the object, so the object slows down)

2) the correct answer is increases.

In fact, the centripetal acceleration is given by
$a_c = \frac{v^2}{r}$
where v is the velocity and r the radius. From the formula, we see that if the radius r decreases, the centripetal acceleration increases.

2b) the correct answer is 2times.

In fact, the centripetal acceleration is given by
$a_c = \frac{v^2}{r}$
where v is the velocity and r the radius. If the radius is decreased to one half:
$r'= \frac{1}{2}r$
the new centripetal acceleration is
$a_c = \frac{v^2}{ r' }= \frac{v^2}{ \frac{1}{2}r } =2 \frac{v^2}{r}=2 a_c$
which means that the centripetal acceleration is changed to 2 times its original value.