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.