in this section we're going to discuss how forces affect linear movement linear movement is the movement of the object with no rotation of the object you'll encounter movements of objects many times in your program for instance single electrons move due to the effect of electric and magnetic fields consider a cart moving along the road this is an example of linear motion but of course within the cart the wheels rotate motion and force are intimately linked so to understand motion first we need to identify the forces on the car the main force is the weight gravity pulling it downwards the formula for weight is the mass times the gravitational field strength which is a constant on Earth make sure you don't confuse weight and mass in the Ordinary World we often discuss the weight of something but give a value with a units of mass kilog or tons technically you should give your weight in Newtons not kilog but because G is a constant once you know the mass you can calculate the weight forces are usually drawn as arrows we now see three types of forces here apart from the weight we have the thrust from the car engine pull in the cart and there are also reaction forces between the cart and the wheels and the wheels in the road to work out the resultant Force we need to add the forces as vectors to do this we draw the force arrows from a single point called the the center of mass this is standard practice when considering the movement of the whole object as we are here now let's consider a very simple scenario where the cart is stationary since there is no pulling or braking forces acting on the cart we're left with the weight downwards and the reaction forces upwards we know that the cart doesn't move up and down so we can conclude that the reaction forces balance the weight at this point all the forces on the car add vectorially to zero we may therefore state that the object is in equilibrium now let us do something more exciting the car now accelerates thus producing a pulling force in balancing the equilibrium of forces pulling the cart forward if we plot how the cart speed changes with time we get a straight line graph note that we're using the letter V which stands for velocity however technically velocity is a vector so here we only concern ourselves with the magnitude of the Velocity in this case when the speed increases linearly with time we may calculate the acceleration as Delta V over delta T this will give us the slope of the straight line shown in the graph however in more general terms we Define acceleration as DV by DT that is we make the Delta infinately small this enables us to deal with situations where the speed does not change linearly with time let's imagine now that the car is not at rest but already traveling at a speed V at time T let's now calculate the slope of the graph if we rearrange the formula for acceleration and set T not to be zero we find a formula for the final velocity that depends on the starting velocity the acceleration and time this is known as one of the constant acceleration formulas now that we have a formula for V we can also calculate how far the car goes we do this by integration velocity is the change in distance with time so we integrate to find the distance in the equation resulting from the integration the main feature is that the distance increases quadratically with time let's see what affects acceleration first of all let's change the mass by loading the car we find that the slope decreases this means the acceleration is inversely proportional to the mass if we put a more powerful engine in the car this provides more Force we find the slope now increases this shows that the acceleration is proportional to the force combining the knowledge of how mass and force affect the acceleration gives a well-known equation FAL ma let's now look at the situation where the car is moving but there is no pulling force on the car from the car we find that the car stays at the same speed on our graph this important result shows that without acceleration an object remains at a constant velocity we can do a quick calculation of how far the car travels when coasting by setting acceleration to zero in our distance equation we see that the distance traveled is now linear in time now let's think about slowing down when the car breaks this is a negative acceleration we can tell this by using the constant acceleration formula and setting V2 to zero and find that the acceleration is indeed negative looking at the whole journey we see the acceleration and deceleration gives a quadratic speed up and slow down while no acceleration gives a linear increase in distance of course the grass we plot of the car are not realistic air resistance and friction are extra forces we haven't taken into account these are more complex because they depend on the speed of the car itself this means we cannot use the constant acceleration formula so why use a simple picture of constant forces it means we can identify the three laws of linear motion Newton's Laws these describe in simple terms how objects behave it's also important to understand how energy changes when objects move one of the most important forms of energy is kinetic energy when an object is in motion kinetic energy is proportional to mass and to the square of the Velocity energy is conserved it does not disappear but is converted to different forms for instance when a car goes up a hill its kinetic energy transformed into potential energy