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: