Once upon a time, a famous zoologist was hunting antelope for a zoo with a dart gun that fired darts with a range of 100 m at a speed of 25 m/s. If he shot a dart at an antelope at rest 50 m away, and the antelope instantly began to accelerate at a constant rate away from the dart, running out of range of the dart just in time:
a) Find the minimum acceleration of the antelope.
b) Find the maximum time the antelope can remain in range of the dart.
c) Find the minimum speed of the antelope as it runs out of range of the dart.