Question
Derive $\text{x}_2=\text{x}_1+\text{v}_1(\text{t}_2-\text{t}_1)+\frac{1}{2}\text{a}(\text{t}_2-\text{t}_1)^2.$
✓
Answer
Consider a body starting from x1 and reaching x2 at time t2. Starting with a velocity v1 at time t1 with a uniform acceleration ‘a'. The motion can be described by the v-t graph as shown. Area below v-t graph is PMWYNP $=\text{WM}\times\text{WY}\times\frac{1}{2}\text{WY}\times\text{NP}$ $=\text{v}_1(\text{t}_2-\text{t}_1)+\frac{1}{2}(\text{t}_2-\text{t}_1)\times(\text{v}_2-\text{v}_1)$ Since area below v-t graph is displacement and v2 - v1 = a(t2 - t1), we get $\text{x}_2-\text{x}_1=\text{v}_1(\text{t}_2-\text{t}_1)+\frac{1}{2}(\text{t}_2-\text{t}_1)\times\text{a}(\text{t}_2-\text{t}_1)$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Explain why:
The coolant in a chemical or a nuclear plant (i.e., the liquid used to prevent the different parts of a plant from getting too hot) should have high specific heat.
The coolant in a chemical or a nuclear plant (i.e., the liquid used to prevent the different parts of a plant from getting too hot) should have high specific heat.
Is it necessary for the plane of the orbit of a satellite to pass through the centre of the earth?
Explain the difference between weight and mass.
Convert 1 Joule of energy into CGS system.
Two cylinders A and B of equal capacity are connected to each other via a stopcock. A contains a gas at standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. The stopcock is suddenly opened. Answer the following:
What is the change in the temperature of the gas?
What is the change in the temperature of the gas?
A block of mass 1kg is placed at the point A of a rough track shown in figure. If slightly pushed towards right, it stops at the point B of the track. Calculate the work done by the frictional force on the block during its transit from A to B.
The energy E of a photon and its frequency u are expressed by the relation E = hv. State the dimensions and unit of Planck's constant h.
What is the significance of:
- Wetting agents used by dyers.
- Water proofing agents?
The radius of atom is of the order of $2\mathring{\text{A}}$ and radius of a nucleus is of the order of fermi. How many magnitudes higher is the volume of atom as compared to the volume of nucleus?
→Explain the reason why the liquid rise to a higher height in the capillary tube when its diameter decreases.