1. a car traveling at 10 m/s starts to decelerate steadily. it comes to a complete stop in 20 seconds. what…

1. a car traveling at 10 m/s starts to decelerate steadily. it comes to a complete stop in 20 seconds. what is its acceleration? 2. an airplane travels down a runway for 4.0 seconds with an acceleration of 9.0 m/s². what is its change in velocity during this time? 3. a child drops a ball from a bridge. the ball strikes the water under the bridge 2.0 seconds later. what is the velocity of the ball when it strikes the water? 4. a boy throws a rock straight up into the air. it reaches the highest point of its flight after 2.5 seconds. how fast was the rock going when it left the boy’s hand?

1. a car traveling at 10 m/s starts to decelerate steadily. it comes to a complete stop in 20 seconds. what is its acceleration? 2. an airplane travels down a runway for 4.0 seconds with an acceleration of 9.0 m/s². what is its change in velocity during this time? 3. a child drops a ball from a bridge. the ball strikes the water under the bridge 2.0 seconds later. what is the velocity of the ball when it strikes the water? 4. a boy throws a rock straight up into the air. it reaches the highest point of its flight after 2.5 seconds. how fast was the rock going when it left the boy’s hand?

Answer

Explanation:

Step1: Recall acceleration formula

The formula for acceleration is $a=\frac{v - u}{t}$, where $v$ is final - velocity, $u$ is initial - velocity, and $t$ is time. For the car, $u = 10\ m/s$, $v = 0\ m/s$, and $t = 20\ s$. $a=\frac{0 - 10}{20}$

Step2: Calculate car's acceleration

$a=\frac{- 10}{20}=-0.5\ m/s^{2}$

For the airplane, the formula for change in velocity is $\Delta v=a\times t$. Given $a = 9.0\ m/s^{2}$ and $t = 4.0\ s$. $\Delta v=9.0\times4.0 = 36\ m/s$

For the ball dropped from the bridge, we use the formula $v = u+gt$. Since it is dropped, $u = 0\ m/s$ and $g = 9.8\ m/s^{2}$, $t = 2.0\ s$. $v=0 + 9.8\times2.0=19.6\ m/s$

For the rock thrown up, at the highest - point the final velocity $v = 0\ m/s$. Using the formula $v = u - gt$ (negative because the acceleration due to gravity acts downwards), $g = 9.8\ m/s^{2}$, $t = 2.5\ s$. $0 = u-9.8\times2.5$, so $u=9.8\times2.5 = 24.5\ m/s$

Answer:

  1. The car's acceleration is $-0.5\ m/s^{2}$.
  2. The airplane's change in velocity is $36\ m/s$.
  3. The ball's velocity when it strikes the water is $19.6\ m/s$.
  4. The rock's initial velocity when it left the boy's hand is $24.5\ m/s$.