A constant force is applied to an object, causing the object to accelerate at 10 m/s². What will the acceleration be if

a. The force is halved?

Question

A constant force is applied to an object, causing the object to accelerate at 10 m/s². What will the acceleration be if

a. The force is halved?

Accepted Answer

Everyone in this problem, the tires of a pickup truck push against the road with a uniform force accelerating the truck at 6.5 m/s squared. Were asked to determine the new acceleration When the force between the road and tires is reduced to 3/4 of the original value. So we're giving information about a force and acceleration. And so what we want to do is think about Newton's law, need to relate the two. Newton's law tells us that the sum of the forces is equal to the mass multiplied by the acceleration. So initially, we have some force and we're going to call it F1, this is a uniform force and it accelerates the truck at 6.5 m per second squared. And so we have F one is equal to the mass and we're going to call it M T the mass of the truck multiplied by the acceleration of 6.5 m per second squared. Alright, that's all the information we know about that initial case. Now the new acceleration. Well, we're gonna have some new force, we still have the same mass. So we have the mass of our truck, which is the same and that's multiplied by this new acceleration. A new, We're told in the problem that the force between the road and tires is reduced to three quarters of the original value. And so f new, the new force is going to be equal to three fourths Multiplied by F one, the initial force and that's equal to the mass of the truck empty, multiplied by the new acceleration. A new recall that we're looking for that new acceleration. Alright. Well, what is F one? We had an expression for F one. Let's go ahead and substitute it in. So we get 3/4 multiplied by the mass of the truck multiplied by 6.5 meters per second. Squared is equal to the mass of the truck multiplied by the new acceleration. And now what you'll see is we can divide by the mass of the truck. Here, we have that term on both sides. We can divide and it's going to cancel, which is good. We didn't have the value of the mass of the truck. So the fact that we're able to do that means that we can get a value for our acceleration. And so our new acceleration, a new is equal to 3/ multiplied by 6.5 m per second squared, Which gives us a value of 4.8, m/s squared. That is the new acceleration of the truck. So if we go up to our answer choices. We see that the answer choices are rounded to three significant digits. So if we take our answer around it to three significant digits, we see that the new acceleration of the truck when the force is reduced to three quarters of the original value is going to be a 4.88m/s squared. That's it for this one. Thanks everyone for watching. See you in the next video.

A constant force is applied to an object, causing the object to accelerate at 10 m/s². What will the acceleration be if a. The force is halved?

Verified Solution

Key Concepts

Newton's Second Law of Motion

Acceleration

Force and Mass Relationship