acar traveling along a straight roed increases it's speed from 30m/s to 50m/s a distance of 300m .If the acceleration is constant how much time elapses while the car moves this distance?

Answer 1

Use the kinematic formula vf^2=vi^2+2ad.

50^2=30^2+2*a*300

Solving for "a" gives 2.67 m/s/s, or 3 m/s/s if you must use significant digits.

Remember that when you have 3 knowns and acceleration is constant, you can use kinematics to find an unknown.

Answer 2

constant acceleration means speed is linear with time
v = 30 + a t
that means you can use the average speed, 40 m/s
300 m / 40 m/s = 7.5 seconds
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proof it works:
50 = 30 + a t so a t = 20 and t = 20/a

300 = 30 t + .5 a t^2
300 = 30 (20/a) + .5(20)(20)/a
300 = 40 (20/a)
300 a = 800
a = 8/3
then t = 20 * 3/8 = 7.5 seconds sure enough