Hints offered by K Russell, with video solutions by 'DLBmaths'

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Paper 1

Question 1

Hint 1: Use F = ma

Hint 2: Use a constant acceleration equation

Hint 3: and here is a video of the solution:

Question 2

Hint 1: Resolve in the x and y directions

Hint 2: Solve the simultaneous equations

Hint 3: and here is a video of the solution:

Question 3

Hint 1: Find displacement

Hint 2: Use WD = F.s

Hint 3: and here is a video of the solution:

Question 4

Hint 1: Use the product rule for differentiation

Hint 2: and here is a video of the solution:

Question 5

Hint 1: Use one of the formulae on the formula sheet and both sets of conditions to form two equations

Hint 2: Divide one equation by the other

Hint 3: and here is a video of the solution:

Question 6

6b)i) Hint 1: Know the area under a v-t graph is the distance travelled

Hint 2: and here is a video of the solution:

Question 7

Hint 1: Max speed occurs when a = 0

Hint 2: Integrate acceleration to find velocity

Hint 3: and here is a video of the solution:

Question 8

8a) Hint 1: Use algebraic long division

8b)i) Hint 2: Apply the general form of the partial fractions

8b)i) Hint 3: Make substitutions for x to find the constants

Hint 4: and here is a video of the solution:

Question 9

9a) Hint 1: Resolve radially with F = ma and resolve vertically

9a) Hint 2: Divide one equation by the other and rearrange for v

Hint 3: and here is a video of the solution:

Question 10

10a) Hint 1: Find dx/dt and dy/dt

10b) Hint 2: When t = 0, find dy/dx and use m = tan(θ)

Hint 3: and here is a video of the solution:

Question 11

Hint 1: Use the formulae for centre of mass of a lamina using calculus

Hint 2: and here is a video of the solution:

Question 12

12a) Hint 1: Draw a triangle of velocities

12a) Hint 2: Use the cosine rule

12b)ii) Hint 3: Draw a new triangle of velocities and apply sine and cosine rules

Hint 4: and here is a video of the solution:

Question 13

13a) Hint 1: Apply formula for volume of revolution about the x axis

13b) Hint 2: Use half the volume from part (a) and integrate with unknown upper limit

Hint 3: and here is a video of the solution:

Question 14

Hint 1: Resolve parallel and perpendicular to the plane for both situations

Hint 2: Combine equations for parallel and perpendicular for each situation and rearrange for μ

Hint 3: Equate expressions for μ and rearrange for P

Hint 4: and here is a video of the solution:

Question 15

15a) Hint 1: Use F = ma

15b) Hint 2: Set up auxiliary equation and write the general solution

15b) Hint 3: Differentiate the general solution and apply the conditions

Hint 4: and here is a video of the solution:

Question 16

16a) Hint 1: Use constant acceleration equations horizontally and vertically

16a) Hint 2: Rearrange horizontal equation for t and substitute into the vertical equation

16b) Hint 3: Use y = h and x = 4h to form an equation

16b) Hint 4: Use y = h and x = 5h to form another equation

16b) Hint 5: Get both equations in a form to equate them and solve for θ

Hint 6: and here is a video of the solution:

Question 17

17a)i) Hint 1: Use conservation of energy

17a)ii) Hint 2: Resolve radially with F = ma

17a)ii) Hint 3: Apply conditions that θ = 180 and T > 0

17b) Hint 4: When the string goes slack, T = 0

17b) Hint 5: Rearrange for cos(θ) and substitute into height expression

Hint 6: and here is a video of the solution:

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