(Solved): 5. The diagram below shows a speed time graph of an object which starts from rest and accelerat ...

5. The diagram below shows a speed time graph of an object which starts from rest and accelerates at a uniform rate for 8 seconds until it reaches $m$ metres per second. It then assumes a different uniform acceleration until it reaches $\mathbf{n}$ metres per second. It finally retards uniformly and eventually come to rest. (i) Find the value of $m$ if the acceleration during the first $8s$ was $3\mathrm{m}/{\mathrm{s}}^2$. (ii) Calculate the value of $\mathrm{n}$ given that the total distance covered between the $8^{\text{th }}$ and $18^{\text{th }}$ second is $345\mathrm{m}$. (iii) Find the value of $\mathbf{T}$ if retardation was $5\mathrm{m}/{\mathrm{s}}^2$. 6. (a) Define the following in relation to angular motion; (i) Radian (ii) Angular displacement (iii) Angular velocity (iv) Angular acceleration (b) A grinding wheel of diameter $30\mathrm{cm}$ and rotating at $47.75\mathrm{rev}/\min$ accelerates uniformly at 0.5 rads ${}^{-2}$ for $30\mathrm{s}$. Find: (i) The final angular velocity (ii) The final peripheral (circumferential) speed (iii) The angle turned through by the wheel during this time.