Question

a truck with an overall mass of 6500 kg is accelerating at 0.3 m/s². what force does the engine need to apply in order to do this? a person is riding a bike and accelerating at 2.8 m/s² with a force of 100 n. what is the mass of the rider and bicycle? a 35 kg child jumps on a trampoline on the moon and becomes airborne. they hit the trampoline safely with a force of 20 n. what was their downwards acceleration? a carnival bumper car with a mass of 300 kg accelerates at 0.3 m/s² towards a wall. what is the force on the car before impact? a boulder is dropped from a cliff and hits the ground. its acceleration was 9.81 m/s² and the force on the boulder was 300 n. find the mass of the boulder. a 1300 kg tomahawk land attack missile erupts from the water, initially propelled by a solid propellant with a force of 400000 n. what will be the acceleration due to this propellant? a 85 kg runner waits at the starting line. what force is required reach an acceleration of 3.4 m/s²? a 50.5 n force is applied to a golf ball, generating an initial acceleration of 15 m/s². calculate the mass of the golf ball. what would be the acceleration of a launched projectile from a trebuchet with a 35 kg mass when the force used is 1000 n?

Explanation:

Step1: Recall Newton's second - law formula

$F = ma$, where $F$ is force, $m$ is mass and $a$ is acceleration.

Step2: Solve the first problem (truck)

Given $m = 6500$ kg and $a=0.3$ m/s². Substitute into $F = ma$.
$F=6500\times0.3 = 1950$ N

Step3: Solve the second problem (bike - rider)

Given $F = 100$ N and $a = 2.8$ m/s². Rearrange $F = ma$ to $m=\frac{F}{a}$.
$m=\frac{100}{2.8}\approx35.71$ kg

Step4: Solve the third problem (child on trampoline)

Given $m = 35$ kg and $F = 20$ N. Rearrange $F = ma$ to $a=\frac{F}{m}$.
$a=\frac{20}{35}=\frac{4}{7}\approx0.57$ m/s²

Step5: Solve the fourth problem (bumper - car)

Given $m = 300$ kg and $a = 0.3$ m/s². Substitute into $F = ma$.
$F=300\times0.3 = 90$ N

Step6: Solve the fifth problem (boulder)

Given $F = 300$ N and $a = 9.81$ m/s². Rearrange $F = ma$ to $m=\frac{F}{a}$.
$m=\frac{300}{9.81}\approx30.58$ kg

Step7: Solve the sixth problem (Tomahawk missile)

Given $m = 1300$ kg and $F = 400000$ N. Rearrange $F = ma$ to $a=\frac{F}{m}$.
$a=\frac{400000}{1300}=\frac{4000}{13}\approx307.69$ m/s²

Step8: Solve the seventh problem (runner)

Given $m = 85$ kg and $a = 3.4$ m/s². Substitute into $F = ma$.
$F=85\times3.4 = 289$ N

Step9: Solve the eighth problem (golf ball)

Given $F = 50.5$ N and $a = 15$ m/s². Rearrange $F = ma$ to $m=\frac{F}{a}$.
$m=\frac{50.5}{15}=\frac{101}{30}\approx3.37$ kg

Step10: Solve the ninth problem (projectile)

Given $m = 35$ kg and $F = 1000$ N. Rearrange $F = ma$ to $a=\frac{F}{m}$.
$a=\frac{1000}{35}=\frac{200}{7}\approx28.57$ m/s²

Answer:

Truck force: 1950 N
Bike - rider mass: 35.71 kg
Child acceleration: 0.57 m/s²
Bumper - car force: 90 N
Boulder mass: 30.58 kg
Missile acceleration: 307.69 m/s²
Runner force: 289 N
Golf - ball mass: 3.37 kg
Projectile acceleration: 28.57 m/s²