Question

When a driver presses the brake pedal, his car can stop with an acceleration of 5.4 m/s2. How far will the car travel while coming to a complete stop if its initial speed was 25 m/s?

A.25.1 m
B.2.31 m
C.57.9 m
 D.101.4 m

Answer 1

Using the kinematic equation for uniformly accelerated motion, the car will travel approximately 57.9 meters while coming to a complete stop. The correct answer is option C.

To find out how far the car will travel while coming to a complete stop, we can use the kinematic equation for uniformly accelerated motion:

v2 = u2 + 2as

Where v is the final velocity (0 m/s since the car comes to a stop), u is the initial velocity (25 m/s), a is the acceleration (-5.4 m/s2, it is negative since it's a deceleration), and s is the distance we need to find.

Rearranging the formula to solve for s, we get:

s = (v2 - u2)/(2a)

Substitute the given values into the equation:

s = (0 - 252)/(2 * -5.4) = (0 - 625)/(-10.8) = 625/10.8 ≈ 57.9 m

So the car will travel approximately 57.9 meters while coming to a complete stop.

The correct answer is C.57.9 m

Answer 2

`Given:\\a=5.4 (m)/(s^2) \\v_0= 25(m)/(s) \\\\Find:\\s=?\\\\Solution:\\\\s=v_0t- (at^2)/(2) \\\\a= (\Delta v)/(t) \\\\v_e=0\Rightarrow \Delta v=v_0\\\\t= (v_0)/(a) \\\\s= (v_0^2)/(a) - (v_0^2)/(2a) =(v_0^2)/(2a) \\\\s= ( (25(m)/(s))2 )/(2\cdot 5.4 (m)/(s^2) ) \approx 57.9m\\\\C\rightarrow Correct\;answer`