Question
Show by using the graphical method that:
$\text{s}=\text{ut}+\frac{1}{2}\text{at}^2$
where the symbols have their usual meanings.✓
Answer
Consider the velocity-time graph of a body shown in figure. The body has an initial velocity u at a point A and then its velocity changes at a uniform rate from A to B in time t. In other words, there is a uniform acceleration a from A to B, and after time t its final velocity becomes v which is equal to BC in the graph. The time t is represented by OC. 
Suppose the body travels a distance s in time t. In the figure, the distance travelled by the body is given by the area of the space between the velocity-time graph AB and the time axis OC, which is equal to the area of the figure OABC. Thus: Distance travelled = Area of figure OABC = Area of rectangle OABC + area of triangle ABD Now, we will find out the area of rectangle OABC and area of triangle ABD.
Suppose the body travels a distance s in time t. In the figure, the distance travelled by the body is given by the area of the space between the velocity-time graph AB and the time axis OC, which is equal to the area of the figure OABC. Thus: Distance travelled = Area of figure OABC = Area of rectangle OABC + area of triangle ABD Now, we will find out the area of rectangle OABC and area of triangle ABD. - Area of rectangle OADC = OA × OC
= u × t
= ut
- Area of triangle ABD $=\Big(\frac{1}{2}\Big)\times\text{Area of rectangle AEBD}$
$=\Big(\frac{1}{2}\Big)\times\text{AD}\times\text{BD}$
$=\Big(\frac{1}{2}\Big)\text{at}^2$
Distance travelled, s = Area of rectangle OADC + Area of triangle ABD$\text{s}=\text{ut}+\frac{1}{2}\text{at}^2$
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
How is green revolution different from white revolution?
Explain various types of irrigation systems in India. How can efficiency of applied water be increased in agriculture.
There is a large group of materials P which can be divided into three groups Q, R, and S on the basis of their properties. The substances belonging to group Q can be solids, liquids or gases. The solids belonging to group Q are usually electrical insulators. Most of the substances of group R are solids which are good conductors of electricity. The substances belonging to group S are neither insulators like Q nor good conductors like R. The properties of S are intermediate between those of Q and R.
- What could the group of materials P be?
- Name the substances Q. Give two examples of such substances.
- Name the substances R. Write two examples of such substances.
- Name the substances S. Give two examples of such substances.
- Out of Q, R and S, which substances are malleable and ductile?
An elephant weighing 40,000N stands on one foot of area 1000cm2 whereas a girl weighing 400N is standing on one ‘stiletto’ heel of area 1cm2.
- Which of the two, elephant or girl, exerts a larger force on the ground and by how much?
- What pressure is exerted on the ground by the elephant standing on one foot?
- What pressure is exerted on the ground by the girl standing on one heel?
- Which of the two exerts larger pressure on the ground: elephant or girl?
- What is the ratio of pressure exerted by the girl to the pressure exerted by the elephant?
Classify connective tissue and give one example of each type.
In a reaction, 5.3g of sodium carbonate reacted with 6g of acetic acid. The products were 2.2g of carbon dioxide, 0.9g water and 8.2g of sodium Q acetate. Show that these observations are in agreement with the law of conservation of mass. sodium carbonate + acetic acid → sodium acetate + carbon dioxide + water.
A car is travelling along the road at 8ms-1. It accelerates at 1ms-2 for a distance of 18m. How fast is it then travelling?
Describe an experiment to show that sound cannot pass through vacuum.
Name two indigenous and two exotic breeds of poultry. Write a note on egg production and broiler production.
What are the different tissues in alimals.