An unwary football player collides with a padded goalpost while running at a velocity of 5.50 m/s and comes to a full stop after compressing the padding and his body 0.450 m. (a) How long does the collision last? What is his deceleration?
a=v²/2s= 5.5²/2•0.45 = …
t=v/a=….
654
To find the time it takes for the collision to last, we can use the equation of motion:
v^2 = u^2 + 2as,
where:
v = final velocity (0 m/s, since the player comes to a full stop),
u = initial velocity (5.50 m/s),
a = acceleration (deceleration, in this case),
s = displacement (0.450 m).
Rearranging the equation, we have:
a = (v^2 - u^2) / (2s).
Plugging in the values, we get:
a = (0^2 - 5.50^2) / (2 * 0.450).
Simplifying further:
a = (-30.25) / 0.900.
a = -33.61 m/s^2.
The negative sign indicates that the acceleration (deceleration) is in the opposite direction to the initial velocity.
The deceleration is calculated to be -33.61 m/s^2.
To find the time, we can use the equation of motion:
v = u + at,
where:
v = final velocity (0 m/s),
u = initial velocity (5.50 m/s),
a = acceleration (-33.61 m/s^2),
t = time.
Rearranging the equation, we have:
t = (v - u) / a.
Plugging in the values, we get:
t = (0 - 5.50) / (-33.61).
t = -5.50 / -33.61.
t = 0.1634 seconds.
Therefore, the collision lasts approximately 0.1634 seconds.